There are several key components that cause students to fail, just as they begin the subject, Pre-Algebra.
One of these key components is understanding what a variable is and is not.
According to everyone else, Algebra is a word that describes something we want to figure out; something we don't know, yet, or solving for unknowns. Ouch that just hurt my head to think about! Ok, ok, that doesn't tell you much, does it? Let's try to look at it in a bit different way, shall we?
Do you recall when you were growing up, and they taught you how to add and subtract? They used a blank line or a little box after the equal sign. The teacher would write the numbers on the board, and then she would write the box or line. She would write things like 3 + 4 = ___. Or, maybe she wrote 3 + ___ = 7. As time went on, she would use the same concept for subtraction, multiplication and division. For instance, she would put, 7 x ___ = 49 or 27/9 = ___.
Ok, algebra does the same thing. However, instead of the box or a line, some mathematician decided it would be easier to use a letter. I suspect he did it because it became too confusing to use a bunch of boxes for several different types of equations. Whatever the case, the old lines and boxes were eliminated and letters were left in their place. So, if you think of algebra that way, you will always know that a letter simply means a box.
Now, let's try using this in an algebraic equation, and see how it works. Remember the 3 + 4 = ___ example, above? Let's try replacing the line with letters: 3 + 4 = X (I just picked the letter 'x' because most times, mathematicians use 'x', 'y' and 'z' instead of the old faithful box or line. So, our answer would be: x = 7.
Confused? Watch: '3 + 4 = __ ' is the same as saying: '3+4 = X' Well, 3 + 4 = 7 so: x = 7 See? That was easy, wasn't it? Now, let's try another example: 2 + X = 5. In this case, it's also fairly easy to figure out that X = 3, because 2 + 3 = 5. That's all a variable really is. It takes the place of the __ or the box. Simple, isn't it?
Algebra really isn't all that difficult, at least if you know what each word and symbol really means. Once you do, it's a breeze. :)
Have a great day, everyone!